Paradigms in Physics: Quantum Fundamentals

Course name:
Paradigms in Physics: Quantum Fundamentals
Course number:
PH 425
Course credits:
3
Class meeting times:
7 hours of lecture per week
Prerequisites:
Recommended PH 213 and concurrent enrollment in MTH 341
Course description:
Introduction to quantum mechanics through Stern-Gerlach spin measurements. Probability, eigenvalues, operators, measurement, state reduction, Dirac notation, matrix mechanics, time evolution. Quantum behavior of a one-dimensional well.

Schedule from 2023:

Day
Topic
Activities
Resources
Homework

Day 1 M 2/7

Welcome to QF!
  • Hello Video
  • Ph425 Student Info
  • Photo Permission

Magnetic Moment
  • face Intro to Magnetic Moment

Stern-Gerlach Experiment: Measuring Electron Spin
  • Spin Fermi Estimate
  • Stern Gerlach Explain

Day 2 Tu 2/8

Explore the Stern-Gerlach Experiment
  • group Intro to Stern-Gerlach Experiments 1
  • computer Binomial Statistics Mathematica
  • Statistical Analysis of the Spins Sim

Quantum State are Vectors
  • face The Quantum State Postulate

Two Sequential SG Experiments
McIntyre 1.2

Three Sequential SG Experiments
  • group Stern-Gerlach & Quantum Eraser
  • face Mixture vs. Superposition
McIntyre 1.2.3

Day 3 W 2/9 Math Bits

Review: Complex Numbers: Rectangular Form
  • Complex Numbers: Rectangular Form

Complex Conjugation
Norm
  • Real Part of a Complex Number

Algebra with Complex Numbers

Review: Circle Trig
  • Circle Trig Practice
  • Circle Trigonometry

Complex Numbers: Exponential Form
  • Circle Trig Complex
  • Complex Conjugate
  • Complex Numbers All Forms Practice
  • Complex Rect Polar Quiz
  • Complex Rectangular Practice
  • Complex Rectangular Practice
  • Euler's Formula
  • Phase
  • Representations of Complex Numbers LO1

Day 4 Th 2/10 Math Bits

Components of Vectors
  • group Describing a Vector with 2 Different Coordinate Systems

Inner Products
  • group Representations of Inner Products
  • Orthogonal
  • Orthogonal Brief

Bra-ket (Dirac) Notation
  • Dirac Practice

Day 5 F 2/11

Inner Product of a Complex Vector

Review the Anatomy of SG Experiments

The Probability Postulate
  • face Probability Postulate
McIntyre 1.2
  • Histogram
  • Measurement Probabilities
  • Phase 2 LO1 LO2

  • assignment_ind Probabilities of \(S_z\) Measurements for Spin-1/2 in Bra-Ket Notation

Day 6 M 2/14

Practice Probability Postulate & Normalization

Determining Spin from Experiments
  • face Determining \(|\pm_x\rangle\) and \(|\pm_y\rangle\) in the \(S_z\) basis
  • Chained Stern-Gerlach

Multiple Representations of Quantum States

Relative & Overall Phase

Day 7 Tu 2/15

Determining Spin from Experiments
  • group Finding Unknown States Leaving the Oven in a Spin-\(\frac{1}{2}\) System
  • Unknowns One Half
  • Unknowns Spin-1/2 Brief

Multiple Representations of Quantum States
  • group Multiple Representations of a Quantum State

Day 8 W 2/16 Mathbits

Review: Operations with Matrices
  • Matrix Refresher
  • Pauli
  • Pauli Practice

More Operations with Matrices
  • Hermitian Adjoints

Linear Transformations
  • group Linear Transformations
  • Commutator
  • Spin Matrix

Day 9 Th 2/17 MathBits

Diagonalization
  • Diagonalization
  • Diagonalization Part II


Day 10 F 2/18 Math Bits

Finding Eigenvectors & Eigenvalues
  • group Finding Eigenvectors and Eigenvalues
  • Eigen Spin Challenge
  • Eigenvectors of Pauli Matrices
  • Eigenvectors of the Rotation Matrix

Eigenbases

Day 11 M 2/21

Properties of Hermitian Matrices

Day 12 Tu 2/22

Intro to Higher Spin Systems
  • face Spin-1
  • General State
  • Spin One Intro

Projection Operators
McIntyre 2.2-2.4

Changing Bases with a Completeness Relation
  • Completeness Relation Change of Basis

Day 13 W 2/23

The Projection Postulate

General Quantum Systems

Quantum Interferometer
  • group Spin-1 Interferometer
  • Spin One Interferometer Brief

Day 14 Th 2/24

Quantum Interferometer Cont.

Quantum Operators
  • group Constructing the Spin Operators

Finding Matrix Elements
  • group Finding Matrix Elements
  • Matrix Elements and Completeness Relations

The Squared Spin Operator
  • Spin Three Halves Operators

Day 15 F 2/25

Commutation
  • Commute

Day 16 M 2/28

Quantum Expectation Values

Quantum Uncertainty

Day 17 Tu 3/1

Solving the Schrodinger Equation & Time Evolution
  • face Solving the Schrodinger Equation

More Time Evolution
  • Probabilities of Energy

Day 18 W 3/2

Spin Precession in a Uniform Magnetic Field
  • Frequency
  • Magnet

Day 19 Th 3/3

Introduction to Wavefunctions
  • Wavefunction Calculations
  • Wavefunctions

Day 20 F 3/4

  • group Going from Spin to Wavefunction (Modified)

Day 21 M 3/7

The Infinite Square Well
  • group Going from Spin to Wavefunction (Modified)
McIntyre 5.3-5.4
  • ISW Expectation
  • ISW Right Quarter

Day 22 Tu 3/8

Wavefunctions
McIntyre 5.1-5.2

Day 23 W 3/9

Time Evolution of a particle in an Infinite Square Well
  • group Time Evolution of the ISW
  • ISW Energy Measurement

Day 24 Th 3/10

Quantum Spookiness

Day 25 F 3/11

Representations of the Infinite Square Well

  • face Final Exam Review Guide

Review

3/17 Th noon-2pm
Final Exam